The expressions equivalent to 4^10 are 2^20, 4^4 . 4^6, and 4^4 / 4^-6. Option B, option C, and option E are correct.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe need to find all the expressions equivalent to 4^10.
We will use laws of exponents for all the options one by one.
Option A:
2^5 . 2^2 = 2^(5 + 2) = 2^7
This is not equivalent to 4^10.
Option B:
2^10 = 2^(2 * 10) = (2^2)^10 = 4^10
This is equivalent to 4^10.
Option C:
4^4 . 4^6 = 4^(4 + 6) = 4^10
This is equivalent to 4^10.
Option D:
4^7 . 4^-3 = 4^(7 + (-3)) = 4^4
This is not equivalent to 4^10.
Option E:
4^4 / 4^-6 = 4^(4 - (-6)) = 4^10
This is equivalent to 4^10.
So, 2^20, 4^4 . 4^6, and 4^4 / 4^-6 are equivalent to 4^10.
So, option B, option C, and option E are correct.
Thus, the expressions equivalent to 4^10 are 2^20, 4^4 . 4^6, and 4^4 / 4^-6. Option B, option C, and option E are correct.
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Suppose that x units of a product cost C dollars to manufacture and earn revenue of R dollars. The value of x at
which the expressions for C and R are equal is the break-even quantity, or the number of units that produce 0
profit. Complete parts (a) and (b) below.
C=84x+1,475; R = 109x
No more than 34 units can be sold.
a) The break-even quantity (in units) is 59 units.
b) If the company is selling no more than 34 units, A. The product should not be produced because it will lead to a loss of $625.
What is the break-even point?The break-even point is the production and sales point at which the total costs equal the total revenue.
At the break-even point, there is no profit or loss.
Total units produced = x
Let the cost of production = C
Let the revenue = R
C = 84x+1,475
R = 109x
At the break-even point, 109x = 84x + 1,475
109x - 84x = 1,475
25x = 1,475
x = 59 units
If x = 34 units:
Total cost = 84x+1,475
= 84(34) + 1,475
= 2,856 + 1,475
= $4,331
Total revenue = 109x
= 109(34)
= $3,706
Loss = $625 ($3,706 - $4,331)
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Question Completion:(a) Find the break-even quantity units (Simplify your answer.)
(b) Decide whether the product should be produced on the basis of whether it will earn a profit. (Profit = Revenue - Cost.)
Choose the correct answer below and, if necessary, in the answer box to complete your choice.
A. The product should not be produced because it will lead to a loss of B. The product should be produced because it will lead to a profit of
7. The area of the shaded triangle in the figure
at the right is 43 square inches. What is the
area of the rectangle?
Area of rectangle is 86 square inches.
What is area of triangle?
In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge.The total area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.What is area of rectangle ?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.Area of triangle = 1/2 * b* h
43 = 1/2 *b * h
86 = b * h
Area of rectangle = Length * Breadth
We know that base of triangle = Breadth of the rectangle and
Height of triangle = length of triangle
So, Area of rectangle is 86 square inches.
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find two numbers such that one number is 4 more than twice as big as the other number and the two numbers sum to 28
The first number is 8 and the second number is 20
let the first number = X
the second number = 4 + 2X
sum = 28
X + (4 + 2X) = 28
3X + 4 = 28
3X = 24
X = 8
The first number is 8
and the second number is 4 + 2X = 4 + 2(8) = 20
Addition:
When we say "the addition," we mean adding two or more numbers together. The plus sign (+) denotes addition of two numbers, therefore three is written as three plus three. You also have control over how often the plus sign (+) is used. such as 3 + 3 + 3 + 3. Mathematical addition is an essential part of children's education. Students learn basic addition sums in primary school, including one-digit facts, math addition sums, and double-digit math addition sums. Sums in addition are one of the most fundamental and fascinating Math concepts for elementary school students. Children first learn fundamental mathematical ideas like adding numbers in their early years because math is an enthralling subject.
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The length of a room is two times it breadth and breadth is three times it's height. If
the area of it's four walls is 288 m², then find the area of it's floor.
Step-by-step explanation:
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The length of a room is
3
4
times its breadth. The total area of the four walls of this room is
15
28
times the area of the floor of the room. What is the ratio of the height of the room to the length of the room?
Medium
Solution
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Correct option is D)
Let breadth =x units
Then length =
3
4
x units
⇒ Area of floor = x×
3
4
x=
3
4
x
2
square units
Let the height of the room =y units. Then
Area of four walls = 2[xy+
3
4
xy]=
3
14
xy
Now,
3
14
xy=
15
28
(
3
4
x
2
)⇒xy=
15
2
×4x
2
y=
15
8
x ⇒
x
y
=
15
8
⇒ y:x=8:15
First place pays $4800 to the winner, second place $3300 and third place $1300. Is it worthwhile to enter the race if it costs $1000?
It is worthwhile to enter the race if it costs $1000.
What is total cost?Total cost is an economic measure that includes not only the initial cash outlay but also the opportunity cost of their choices when producing a product, purchasing an investment, or acquiring a piece of equipment. TVC + TFC = TC
The sum of fixed and variable costs is the total cost. For example, if a company has a fixed cost of $30 per unit and a variable cost of $5 per unit as output increases, the total cost is $35.
In this case, first place pays $4800 to the winner, second place $3300 and third place $1300. It is therefore worthwhile since the amounts are more than $1000.
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11,12,13,14 10th term
The value of the 10th term for the sequence 11,12,13,14 is 20.
How to find the term?It's important to note that this is an arithmetic sequence. The formula for an arithmetic sequence is:
= a + (n - 1)d
where a = first term = 11
d = common difference = 1
n = number of terms = 10
The 10th term will be:
= a + (n - 1)d
= 11 + (10 - 1)1
= 11 + (9 × 1)
= 11 + 9
= 20
The value is 20.
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Complete question
The first four terms of an arithmetic sequence are 11,12,13,14. Find the 10th term.
HELP PLEASE If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’, what will be the coordinate of D’?
According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)
Quadrilateral
Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.
Given,
If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.
Here we need to find the coordinate of D'.
In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.
While we looking into the graph, we have identify the point of
A (0,0), B(-4, 3), C(1,5) and D(2,3)
Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).
According to this rule, the new coordinates are written as,
A(0,0) = A'(0,0)
B'(-4,3) = B'(-3,-4)
C(1,5) = C'(5, -1)
D(2,3) = D' (3, -2)
Therefore, the new coordinate of D' is (3, -2).
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geometry lesson!! please help, i’ll make brainliest!
Answer:
GH = 42 ftStep-by-step explanation:
GivenCongruent isosceles trapezoids ABCD and EFGH.SolutionWe know that corresponding parts of congruent figures are congruent.
It means:
AB = CD = EF = GH = 42 ftsomeone help tyyyyyy
A drilling crew dug to a height of 232 feet during their first day of drilling. On the second
day, the crew dug down 193 feet more than on the first day. Describe the height of the
bottom of the hole after the second day.
Answer using a mixed number and label your
answer.
The depth of the bottom of the hole after the second day is 425 feet using addition operation.
What is addition?
In math, addition is the process of adding two or more integers together. The terms addends and sum describe the input and output of the addition operation, respectively.
Given the depth on the first day is 232 feet.
Depth on the second day = 193 feet more than on the first day i.e. 193 feet + depth on the first day
This implies, depth on the second day = 193+232
= 425 feet
The hole's bottom will therefore be 425 feet deep after the second day.
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Please help I was sick and missed out on class.Thank you
Answer:
The slope is -1.
Step-by-step explanation:
When given two points, the formula for slope is [tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].
4 - 7 / -2 - (-5) = -3 / 3
-3 / 3 = -1, so the slope is -1.
z varies directly as x2 and inversely as y2. If z=76 when x=5 and y=2, find z if x=9 and y=9. (Round off your answer to the nearest hundredth.)
[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \begin{array}{llll} \textit{\small "z" varies directly with }x^2\\ \textit{\small and inversely with }y^2 \end{array}}{ z=\cfrac{kx^2}{y^2}}\qquad \textit{we know that} \begin{cases} z=76\\ x=5\\ y=2 \end{cases} \implies 76=\cfrac{k(5)^2}{(2)^2} \\\\\\ 76=\cfrac{25k}{4}\implies \cfrac{4}{25}\cdot 76=k\implies \cfrac{304}{25}=k~\hfill \boxed{z=\cfrac{304x^2}{25y^2}} \\\\\\ when \begin{cases} x=9\\ y=9 \end{cases}\implies z=\cfrac{304(9)^2}{25(9)^2}\implies z=\cfrac{304}{25}\implies z= 12.16[/tex]
The ratio of T-shirts to jumpers in Jacob's wardrobe is 8 : 7.
There are 24 T-shirts in his wardrobe. How many jumpers are there?
Answer:
24:23
Step-by-step explanation:
how many elements are in the set AnB
Answer:
option A - 2
Step-by-step explanation:
event A { 2 4 6 8 10 12 }
event B { 3 6 9 12 }
The set AnB means A intercept B, which simply means all the elements that are common in event A and event B
So we just have to look at all the elements in A and B, we can see that the common elements are 6 and 12 so therefore:
set AnB = { 6 12 }
and the number of elements in set AnB is 2
One equation for calculating the volume of a cylinder is V = B , where B represents the area of the base of the cylinder. Which expression can be used to find the value of B, in square centimeters, for this cylinder?
The numbers are 12.1 and 3.8
The base of a cylinder is circular and it's area is given as B= πr^2
What is a cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
The base of a cylinder is circular . If the base area is B, then the area of the base is πr^2.
where r is the radius of the circle and π is 22/7
The volume of a cylinder is V = B × h
where B is the base area and h is the height or length of the cylinder.
Therefore the volume of a cylinder is V= πr^2h
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Triangle A'B'C' is the image of AABC under a reflection. Given A(-2, 5), B(0, 9), C(3, 7), A'(5,-2), B'(9, 0), and C(7,3), what is the line of reflection?
For given transformation of ΔABC to ΔA'B'C' the line of reflection is x = y
Triangle A'B'C' is the image of ΔABC under a reflection.
Given A(-2, 5), B(0, 9), C(3, 7),
A'(5,-2), B'(9, 0), and C'(7,3)
We need to find the line of reflection.
We can observe that the coordinates (x, y) of preimage are transformed to (y, x) in image.
This means, the line of reflection is x = y
Therefore, for given transformation of ΔABC to ΔA'B'C' the line of reflection is x = y
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A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling
a number less than 12.
The probability of rolling a number less than 12 is 91.6%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
each case in the set is mutually exclusive with the others in the set, the probability that any one of its components will occur is equal to the sum of its component probabilities.
We can have the number 12, the probality will be 1/12
So the probability of rolling a number less than 12 is = (1 - probability of 12)
=1-1/12
=11/12
=0.916
Hence the probability of rolling a number less than 12 is 91.6%.
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Between which two numbers will you find |-2.65|?
A. -2.6 and -2.5
B. -2.7 and -2.6
C. 2.5 and 2.6
D. 2.6 and 2.7
|-2.65| can be found between numbers 2.6 and 2.7
|-2.65| is between which two numbers?
Absolute value means to remove any negative sign in front of a number and to think of the number as positive. This is what the vertical lines | | surrounding -2.65 means.
Thus, |-2.65| = 2.65
If we examine the options, then we can say 2.65 is between 2.6 and 2.7 i.e. 2.6, 2.65, 2.7
Therefore, |-2.65| can be found between the numbers 2.6 and 2.7. So option D is the answer
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Holly is purchasing drinks for a holiday party. She is getting a combination of soda and juice. The soda costs $2 each and the juice costs $5 each. Holly
needs to bring at most 10 drinks but doesn't want to spend more than $50. Which graph shows how many of each type of drink she can buy?
The graph that shows how many of each type of drink she can buy is as shown below.
The correct answer is an option (D)
In this question, we have been given Holly is getting a combination of soda and juice. The soda costs $2 each and the juice costs $5 each. Holly
needs to bring at most 10 drinks but doesn't want to spend more than $50.
Let x be the number of soda cans and y be the number of soda cans(or bottles)
Holly needs to bring at most 10 drinks
So, we get an inequality,
x + y ≤ 10
She doesn't want to spend more than $50.
So, we get an inequality,
2x + 5y ≤ 50
In following graph, an inequality x + y ≤ 10 is represented by blue shaded region and the inequality 2x + 5y ≤ 50 is represented by red shaded region.
The solution set for the given inequalities is represented by a purple region (common region for both the inequalities)
Therefore, the graph that shows how many of each type of drink she can buy is as shown below.
The correct answer is an option (D)
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493÷16
And I need to show my work
Answer: 493/16
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 493 and 16 is 1
Divide both the numerator and denominator by the GCD
493 ÷ 1
16 ÷ 1
Reduced fraction:
493
16
Therefore, 493/16 simplified to lowest terms is 493/16. or 30.8125
write the expressions as the power of 2 (4*2^5)/(2^3*1/16)
The expressions (4×2⁵) / (2³ × 1/16) written as the power of 2 is 2⁸
How to write the expressions as the power of 2?
Given: (4×2⁵) / (2³ × 1/16)
In order to write this expression as the power of 2, we need to use some in indices law:
Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base": 5⁴ x 5³ = 5⁴⁺³ = 5⁷ and P⁴ x P⁶ = P¹⁰
Division law: To divide two variables or numbers with the same base, we need to subtract their powers and raise them to that base": 5¹⁰ ÷ 5³ = 5¹⁰⁻³ = 5⁷ and P⁸ ÷ P² = P⁸⁻² = P⁶
Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:
8⁻² = 1/8² and b⁻⁶ = 1/b⁶
Let's use the laws to create the given expressions as the power of 2:
(4×2⁵) / (2³ × 1/16) = (2²×2⁵) / (2³× 1/2⁴) Note: 4 = 2² and 16 = 2⁴
= (2²⁺⁵) /(2³⁺⁽⁻⁴⁾) Note: 1/2⁴ = 2⁻⁴ (reciprocal law)
= 2⁷ / 2⁻¹
= 2⁷⁻⁽⁻¹⁾ Division law
= 2⁸
Therefore, the expressions as the power of 2 is 2⁸
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What is 5.33333333333 as a fraction?
please help!
Answer:
[tex]5\frac{1}{3} or \frac{16}{3}[/tex]
Step-by-step explanation:
endless 3’s are always 1/3
So now we just add 5 in front of it
5 1/3
Hopes this helps please mark brainliest
[tex]\frac{16}{3}[/tex] is the fraction of 5.3333333.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
We have two types of fractions.
Proper fraction and improper fraction.
A proper fraction is a fraction whose numerator is less than the denominator.
An improper fraction is a fraction where the numerator is greater than the denominator.
Example:
1/2, 1/3 is a fraction.
3/6, 99/999 is a fraction.
1/4 is a fraction.
We have,
5.333333
= [tex]\frac{16}{3}[/tex]
We see that,
3 ) 16 ( 5.333333
15
10
9
10
9
1
and so on...
Thus,
[tex]\frac{16}{3}[/tex] is the fraction of 5.3333333.
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How are the entries of the matrix named by position?
You can ask where you don't understand.
3 of 30 computers are out of seevice what percentage is working
Answer:
10%
Step-by-step explanation:
3/30
1/10
10/100
10%
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What is the perimeter of the shape?
8 ft
15 ft
15 ft
8 ft
ft
Answer: 46 ft
Step-by-step explanation:
You didn't specify what those numbers mean, so I'm going to assume they're the length of the sides of the shape.
The perimeter equals the sum of all sides' lengths of the shape.
So, it equals 8 + 8 + 15 + 15 = 46 ft
find (f o f) x f(x) = 6x+9 and g(x)= x^2
Step-by-step explanation:
given
f(x)=6x+9
solve
6(6x+9)+9=0
36x+54+9=0
36x+63=0
36x=_63
36x/36 = _63/36
x=_63/36
d²y/dx²-3(dy/dx) - 4y = 0
The Solution of the equation y = C₁e⁴ˣ + C₂e⁻ˣ
Derivatives:The derivative of a function is a function that indicates how quickly another function is changing. Differentiation is a term used to describe the process of finding a derivative. In an equation, it is shown as the dependent variable with respect to the independent variable. A value's derivative is a change in value relative to its input. The symbol for a derivative is f'(x).
Here we have
d²y/dx²-3(dy/dx) - 4y = 0
As we know (d/dx) = D
=> D²-3D - 4 = 0
=> D²- 4D + D - 4 = 0
=> D(D - 4) + (D - 4) = 0
=> (D - 4) (D + 1) = 0
=> (D - 4) = 0 and (D + 1) = 0
=> D = 4 and D = -1
Here, roots are real and distinct
Therefore,
Solution of the equation y = C₁e⁴ˣ + C₂e⁻ˣ
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Find the slope, m of the line that passes through the points (-2/3, 3/4) and (5/6, -1/2) Enter your answer as a fraction in simplest form in the box.
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
According to question,
slope = (-1/2-3/4)/(5/6-(-2/3))
slope = (-5/4)/(9/6)
slope = -30/36
slope = -5/6
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
x=25
Step-by-step explanation:
2x-14=36
2x=50
x=25
What is the domain of the function shown on the graph?
Y
4
-8 -6 -4
N
8
6
4
2+
2
4
-6
8-
N
OA. ≤ 2
OB.
x ≤ 1
O C. -10 < x < 2
O D. -8AA ∞
4
6 8
X
The domain of the given graph is x≤ 2, option A is correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
We have to find the domain of the given graph.
Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.
As we observe the graph the value of x are less than 2
Hence, the domain of the given graph is x≤ 2
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